Review Journal 6 Assigned Work: See Website

Transcription

1 MFM2P Polynomial Checklist 1 Goals for this unit: I can apply the distributive law to the product of binomials. I can complete the following types of factoring; common, difference of squares and simple trinomials. U1L1 Getting Ready for Polynomials Learning Goal: I know how to collect like terms and apply the distributive law in algebraic expressions. U5L2 Multiplying Binomials Learning Goal: I can apply distributive law successfully when multiplying binomials and determine their product. U5L3 Common Factoring Learning Goal: I know what a common factor is and I can divide it out of a polynomial to create a product (multiplication question) U5L4 Factoring Difference of Squares Learning Goal: I can spot a difference of squares expression and turn it back into two brackets. U5L5 Factoring Simple Trinomials Learning Goal: I can take a trinomial of the form x 2 +bx+c and turn it back into a product of two brackets. U5L6 Factoring Simple Trinomials With Common Factors Learning Goal: I can factor a simple trinomial that has a common factor, by first taking out the common factor. Note Assigned Work: Page 278, # 1-10 Journal 1 Note Assigned Work: Page 286, (1-4) every other, 6, 9, 10, 15 Journal 2 Note Assigned Work: Page 294, # 1-8, 10, 14, 17, 18 Journal 3 Note Assigned Work: Page 302, #1-8, 10, 14, 17, 18 Journal 4 Note Assigned Work: Page 309, #2-4, 7-13, 15, 17 Journal 5 Note Assigned Work: Page 311, #16 Review Journal 6 Assigned Work: See Website

2 MFM 2P U5L1 Getting Ready for Polynomials Topic : Review of Algebra Concepts Goal : I know how to collect like terms and apply the distributive law in algebraic expressions. 7.0 Get Ready for Polynomials Parts of a term... Names of Polynomials 5x 2 Monomial : Binomial : Trinomial : Polynomial : Multiplying Monomials 5x(3x 2 ) Multiply coefficients and add exponents on the variables. Dividing Monomials Divide coefficients and subtract exponents on the variables. 10x 3 3x 2

3 MFM 2P U5L1 Getting Ready for Polynomials Collecting Like Terms 5x 2 + 4x x - 2x 2 - x + 9 Distributive Law Add the coefficients on anything term that has the same variables and exponents. 2x(x+3) Squaring - (multiplying something by itself) Multiply the monomial through the brackets. (-2) (4x) 2 Practice Page 278 #1-10

4 U5L2 Multiplying Binomials.notebook July 31, 2013 Multiplying Binomials Today's goal: I can apply distributive law successfully when multiplying binomials and determine their product. Recall: Distributive Law 1) 3(x + 5) 2) x(2x 5) 3) 3x(2x + 3) Recall: What is a Binomial? Multiplying Binomials Method 1 Distributive Law Method 2 FOIL (x + 5)(2x 6) (x + 5)(2x 6) Examples: Simplify 1) (2x 5)(3x + 7) 2) (3x 8)(x 5)

5 MFM2P U5L3 Common Factoring Topic : Goal : Common factoring I know what a common factor is and I can divide it out of a polynomial to create a product (multiplication question) 7.2 Common Factoring Common factoring is the process of reversing distributive law. Expand 3x(4x + 1) What math operation ( +, -,, ) did you use to expand the problem? We need to reverse that process. It isn't always easy to see what we should divide back out of the expression. We need to find the Greatest Common Factor of the terms. Finding the GCF of Monomials What is the greatest common factor of... 12x 2 and 18x 3 STEP 1. STEP 1. Determine the GCF of the coefficients STEP 2. STEP 2. Determine variables common to all STEP 3. STEP 3. Determine how many variables they each have in common. Basically you are looking for the lowest exponent. If a variable has no exponent we know it to be one.

6 MFM2P U5L3 Common Factoring Example 1. Determine the GCF for the following expressions. a)12x, 24x 5 b) 14x 3, 35x 2 c) 16x 4, 24x, 40x 6 Reversing Distributive Law (aka Common Factoring) If you are given an expression, you should always look to see if you can DIVIDE something (the same thing) out of every term. 12x 5 + 9x 3-15x STEP 1. STEP 1. Determine the GCF of the terms and place it in front of a set of brackets. STEP 2. STEP 2. Divide the GCF out of each term and put your answer in the brackets. NOTE When you divide out the common factor, you will always have the same number of terms inside the brackets as you started with.

7 MFM2P U5L3 Common Factoring Example 2. Common factor the following. a)10x - 5 b) 20x x c) 8x 4 + 6x 3-2x Example 3. The area of a rectangle is 10x 2-5x. Find an expression for length and width of the rectangle. Homework Page 294 #1-8, 10, 14, 17, 18

8 MFM 2P U5L4 Factoring Difference of Squares Topic : Goal : Factoring I can spot a difference of squares expression and turn it back into two brackets. 7.3 Factoring Difference of Squares Remember what happened when we expanded questions like these.. (x+3)(x-3) (2x+5)(2x-5) (3x-7)(3x+7) The final answer is called a DIFFERENCE OF SQUARES! Both terms are perfect squares, because they come from multiplying something by itself. And the sign is always going to be a minus, because the brackets have different signs. There are three distinct characteristics that make a difference of squares stand out from other factoring questions Remember some of the more common perfect square numbers

9 MFM 2P U5L4 Factoring Difference of Squares A variable is a perfect square as long as the exponent can be split in half (i.e. an even number) Example 1. Find the square root of each of the following, if it is a perfect square x n x x x x x x 2 y 8 Example 2. Spot the difference of squares, and then figure out what brackets they came from (this is called FACTORING) n p p 3-81

10 MFM 2P U5L4 Factoring Difference of Squares Example 3. Sometimes a difference of squares can be disguised by a common factor. If you take the common factor out, then you will see that it can be factored as a difference of squares. 20p x 5-18x 27-12n 2 Homework Page 302 #1-8, 10, 12, 13

11 MFM 2P U5L5 Factoring Simple Trinomials Topic : Goal : Factoring I can take a trinomial of the form x 2 +bx+c and turn it back into a product of two brackets. 7.4 Simple Trinomial Factoring We learned how to expand binomials already by basically using the distributive law twice... (x+5)(x-10) = Now what we want to do is take an expression like x 2-5x - 50 and go back the other way... figure out the two brackets that it came from. We'll start where all mathematicians do - we'll look for a pattern.

12 MFM 2P U5L5 Factoring Simple Trinomials Multiplying Binomials with the SAME SIGNS Expand and Simplify the following. Be sure to order in descending powers of x. (x + 4)(x + 3) (x - 4)(x - 3) When looking for patterns we are going to treat the sign of a term and the number as two separate things. * the sign of the last term is * the sign of the middle term is always positive * the last number is a * the middle number is a product of the constants in the brackets. the same as in the brackets sum of the constants in the brackets. Multiplying Binomials with DIFFERENT SIGNS Expand and Simplify the following. Be sure to order in descending powers of x. (x + 4)(x - 3) (x + 3)(x - 4) When looking for patterns we are going to treat the sign of a term and the number as two separate things. * the sign of the last term is * the sign of the middle term is always negative the same as the bigger constant in the brackets * the last number is a * the middle number is a product of the constants in the brackets. difference of the constants in the brackets.

13 MFM 2P U5L5 Factoring Simple Trinomials Factoring Simple Trinomials x2 + bx + c

14 MFM 2P U5L5 Factoring Simple Trinomials Examples. Use the factoring flow chart to help you factor the following.

15 MFM 2P U5L6 Factoring Simple Trinomials with Common Factors Topic : Goal : Factoring I can factor a simple trinomial that has a common factor, by first taking out the common factor. 7.4 Factoring Simple Trinomials When There's a Common Factor Yesterday we learned to factor something like this... x 2-20x + 36 Sometimes a simple trinomial can look complex, if it has a common factor. 4x 2 + 8x - 96 Once you have taken out the common factor, you can factor the part in the bracket as you would normally factor a simple trinomial.

16 MFM 2P U5L6 Factoring Simple Trinomials with Common Factors We will try a few more and then you can move on to the worksheet. Factor the following expressions fully... 4x 2-20x x 2-22x x 2-3x + 28 x 3 p - 12x 2 p + 32xp 5p 3-80p p k 4-2k 3 + k 2 Homework Page 311 #16 + worksheet (make sure you completed ALL of yesterday's assigned work)

17 -1- n Q2n0X171j MKluCtTaN bskogfstkwtanrxeu 6L9LECS.k r qablrle Ir3iggHhUtNsg crpersveqr fvfewd3.9 3 rm5a6dyes bwu it5h1 RI 0n6fdidnCiftQeQ 3AdlVgdeNbzrqa9 v2w.k Worksheet by Kuta Software LLC MFM 2P Factoring Trinomials Practice n h2 M0b1G1w ukquztkak HStoif1tXwoahrReL nlhlyc5.1 S ta9l4lu 0rJixgMh it gsj arxezssecrxvweqdj.t Factor each completely. 1) x 2 8x 20 2) 5n n 3) m 2 8m ) 6k 3 60k 2 5) 5n n 6) p 3 5p p 7) 6x 3 24x 2 72x 8) x 2 15x ) p 2 + 7p ) 6v v ) 3x x 3 90x 2 12) 2n 3 4n 2 96n 13) k 3 + 5k 2 14) x 3 + 2x 2 15) 2k 2 4k 30 16) k 3 2k 2 + k 17) x x ) 4k 2 76k ) 3n 2 + 3n 36 20) x x ) 3x 2 + 3x ) 4k 4 28k 3 32k 2 23) a a ) 4n 3 16n 2 25) x 2 + 4x 60 26) 5 p 3 80p p 27) 5n 3 25n 2 70n 28) v v ) 6b 2 24b ) v 4 9v 3 31) x 3 14x x 32) n 2 + 8n 9 33) 2x 2 4x 6 34) 5 p 2 5p 10 35) 6b 3 12b 2 144b 36) 6r r + 144

18 -2- f V2K0H1S1R 4KQuvttaH uswoaf3trwiavreen YLXL1CO.2 X majleld nrfiygphztis5 frdepsieer Gv1eqdh.C L omiakd8es DwkibtBhP ji OnYfviqnSiEtyeT NAHlFggeKborxax X2N.l Worksheet by Kuta Software LLC 37) p 2 13p ) b 2 11b ) x 2 + x 20 40) 2x x ) 2x x 2 42) 3 p 3 + 3p 2 18 p 43) 4a a ) n 2 + 5n 50 45) 6r 3 24r 2 192r 46) r 2 + 4r 12 47) n 3 + 4n 2 + 3n 48) 4x 4 16x 3 180x 2 49) 5r r ) 5x 2 25x ) k 3 3k 2 52) 5a 3 65a a 53) x x ) x 2 x 12 55) 6x x ) 6n 2 12n ) 5v 2 5v ) 6k 3 66k k 59) n 2 + n 56 60) p 3 + p 2 20 p 61) a 3 10a 2 + 9a 62) 2x 4 12x 3 63) x x x 64) 4n 2 32n ) 2k 2 18k 66) 3k 2 24k 27 67) v 2 + 5v ) 3k 3 15k k 69) 5x 2 25x ) m 2 4m 21 71) n 3 + 4n 2 21n 72) 4n n ) b 3 b 2 72b 74) x 2 + 9x 75) b 2 + 6b

19 N B2C0h1A1F LKdurtmaR osxoqf1tfw2alrseo 5LNL1Cm.h E ZAslRlL sr0ipg8hotsss frtefsiejr3vsevdw.h 6 gmzaddzeb pwiigteht 9IanwfTiGnZiStLev ZAplggOetbCr HaI H2z.5-3- Worksheet by Kuta Software LLC Answers to Factoring Trinomials Practice 1) (x + 2)(x 10) 2) 5n(n + 5) 3) (m 2)(m 6) 4) 6k 2 (k 10) 5) 5n(n + 8) 6) p(p 3)(p 2) 7) 6x(x 6)(x + 2) 8) (x 5)(x 10) 9) (p + 3)( p + 4) 10) 6(v + 7)(v + 1) 11) 3x 2 (x + 10)(x 3) 12) 2n(n 8)(n + 6) 13) k 2 (k + 5) 14) x 2 (x + 2) 15) 2(k 5)(k + 3) 16) k(k 1) 2 17) (x + 9)(x + 2) 18) 4(k 9)(k 10) 19) 3(n 3)(n + 4) 20) (x + 4)(x + 10) 21) 3(x 6)(x + 7) 22) 4k 2 (k + 1)(k 8) 23) (a + 7)(a + 6) 24) 4n 2 (n 4) 25) (x + 10)(x 6) 26) 5p( p 7)( p 9) 27) 5n(n + 2)(n 7) 28) (v + 6)(v + 10) 29) 6(b 1)(b 3) 30) v 3 (v 9) 31) x(x 6)(x 8) 32) (n + 9)(n 1) 33) 2(x + 1)(x 3) 34) 5( p 2)(p + 1) 35) 6b(b + 4)(b 6) 36) 6(r + 8)(r + 3) 37) ( p 10)(p 3) 38) (b 7)(b 4) 39) (x 4)(x + 5) 40) 2(x + 2)(x + 5) 41) 2x 2 (x + 6) 42) 3 p(p + 3)(p 2) 43) 4(a + 9)(a + 4) 44) (n 5)(n + 10) 45) 6r(r 8)(r + 4) 46) (r 2)(r + 6) 47) n(n + 1)(n + 3) 48) 4x 2 (x + 5)(x 9) 49) 5(r + 8)(r + 9) 50) 5(x 10)(x + 5) 51) k 2 (k 3) 52) 5a(a 6)(a 7) 53) (x + 7)(x + 8) 54) (x + 3)(x 4) 55) 6(x + 10)(x + 9) 56) 6(n 8)(n + 6) 57) 5(v + 7)(v 8) 58) 6k(k 5)(k 6) 59) (n + 8)(n 7) 60) p(p + 5)(p 4) 61) a(a 1)(a 9) 62) 2x 3 (x 6) 63) x(x + 2)(x + 8) 64) 4(n 3)(n 5) 65) 2k(k 9) 66) 3(k + 1)(k 9) 67) (v + 4)(v + 1) 68) 3k(k 4)(k 1) 69) 5(x 1)(x 4) 70) (m 7)(m + 3) 71) n(n + 7)(n 3) 72) 4(n + 2)(n + 5) 73) b(b 9)(b + 8) 74) x(x + 9) 75) b(b + 6)